Question

Please Help Me!!!!! I don"t know what to do! Suppose f (x) = x^3 + x and g(x) = f ^-1(x). Find g'(2).

Answer 1

http://en.wikipedia.org/wiki/Inverse_function#Inverses_and_derivatives

The derivative of inverse = the reciprocal of derivative

\[g'(y) = \frac{1}{f'(x)}\]
f'(x) = 3x^2 + 1

Now to find g'(2) all we need is the "x" value corresponding with y=2
x^3 + x = 2
x^3 +x -2 = 0
(x^2 +x+2)(x-1) = 0
x = 1

\[\rightarrow g'(2) = \frac{1}{3(1)^2 + 1} = \frac{1}{4}\]

Answer 2

THANK YOU!

Answer 3

yw :)